Question

(√5)^log2(3):(√3)^log2(5)

Answer 1

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Answer 2

To simplify the expression (√5)^log2(3) : (√3)^log2(5), we need to compute the values of both terms and then divide them. Let's break it down step by step:

Step 1: Calculate the individual terms. Let's start by calculating the values of (√5)^log2(3) and (√3)^log2(5).

a) (√5)^log2(3): We know that log2(3) is the exponent to which we need to raise 2 to get 3. So, log2(3) is approximately 1.58496.

Now, (√5)^log2(3) can be calculated as follows: (√5)^log2(3) = √(5^log2(3)) = √(5^1.58496)

Using a calculator or approximation, we get: (√5)^log2(3) ≈ √(5^1.58496) ≈ √7.96252 ≈ 2.82017

b) (√3)^log2(5): Similarly, log2(5) is the exponent to which we need to raise 2 to get 5. So, log2(5) is approximately 2.32193.

Now, (√3)^log2(5) can be calculated as follows: (√3)^log2(5) = √(3^log2(5)) = √(3^2.32193)

Using a calculator or approximation, we get: (√3)^log2(5) ≈ √(3^2.32193) ≈ √9.51321 ≈ 3.08458

Step 2: Divide the two terms: Now that we have the values for both terms, we can divide them as follows: (√5)^log2(3) : (√3)^log2(5) = 2.82017 / 3.08458 ≈ 0.91525

So, (√5)^log2(3) : (√3)^log2(5) is approximately 0.91525.